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What is the solution to the expression (1)/(4) - (2)/(3) + (4)/(6)?

Mathematics

ScanSolve AI Answer

Answer

14\frac{1}{4}

Step-by-step solution

6 steps

Here is the solution to the problem:

14−23+46\frac{1}{4} - \frac{2}{3} + \frac{4}{6}

  1. Find the least common denominator (LCD) for the denominators 4, 3, and 6.

    The multiples of 4 are 4, 8, 12, 16...
    The multiples of 3 are 3, 6, 9, 12, 15...
    The multiples of 6 are 6, 12, 18...
    The LCD is 12.

  2. Convert each fraction to an equivalent fraction with a denominator of 12.

    14=1×34×3=312\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} 23=2×43×4=812\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} 46=4×26×2=812\frac{4}{6} = \frac{4 \times 2}{6 \times 2} = \frac{8}{12}

  3. Rewrite the expression with the equivalent fractions.

    312−812+812\frac{3}{12} - \frac{8}{12} + \frac{8}{12}

  4. Perform the operations from left to right.

    First, subtract.

    3−812+812=−512+812\frac{3 - 8}{12} + \frac{8}{12} = \frac{-5}{12} + \frac{8}{12}

  5. Add the fractions.

    −5+812=312\frac{-5 + 8}{12} = \frac{3}{12}

  6. Simplify the resulting fraction.

    312=14\frac{3}{12} = \frac{1}{4}

    The final answer is 14\frac{1}{4}.

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